# An integral with exponential, and trig functions within trig functions

1. May 28, 2013

### b3n5p34km4n

I'm working with the integral from 0 to infinity of

t^(x-1)e^(-atcos(b))cos(atsin(b))

with respect to t. specifically, i'm asked to solve in terms of the gamma function. my question is more of what general technique i should use. all i've been able to do so far is beat it to death using integration by parts, with several different choices for the parts. the main problem i see here is the trig function within the trig function. any insights?

2. May 29, 2013

### SteamKing

Staff Emeritus
Unless b is a function of t, the integrand is t^(x-1) * e^(-A1*t) * cos(A2*t), where A1 = a*cos(b) and A2 = a*sin(b), and both A1 and A2 are constants.

3. May 29, 2013

### pwsnafu

You are integrating with respect to t, so the sin(b) and cos(b) are constants. The trig-inside-a-trig is illusionary.